Question

the figure is a kite. what is the length of the kites longer diagonal? 5 units 35 units 40 units 48 units

Explanation:

Step1: Use the Pythagorean theorem for upper - part right - triangle

Let's consider the upper right - angled triangle formed by half of the shorter diagonal and part of the longer diagonal. The hypotenuse is 13 and one side is 12. By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, if $c = 13$ and $a = 12$, then $b=\sqrt{c^{2}-a^{2}}$.
$b=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5$.

Step2: Use the Pythagorean theorem for lower - part right - triangle

Now consider the lower right - angled triangle. The hypotenuse is 37 and one side is 12. Using the Pythagorean theorem again, if $c = 37$ and $a = 12$, then $b=\sqrt{c^{2}-a^{2}}$.
$b=\sqrt{37^{2}-12^{2}}=\sqrt{1369 - 144}=\sqrt{1225}=35$.

Step3: Calculate the length of the longer diagonal

The length of the longer diagonal of the kite is the sum of the two parts of the longer diagonal calculated above. So the length is $5 + 35=40$ units.

Answer:

40 units